sudo - Failed to connect to Mir: Failed to connect to server socket: No such file or directory

After logging in as another user how do I run GUI programs?

thufir@doge:~$
thufir@doge:~$ sudo -u hawat -i
hawat@doge:~$
hawat@doge:~$ whoami
hawat
hawat@doge:~$
hawat@doge:~$ pwd
/home/hawat
hawat@doge:~$
hawat@doge:~$ echo $HOME
/home/hawat
hawat@doge:~$
hawat@doge:~$ firefox
No protocol specified
Failed to connect to Mir: Failed to connect to server socket: No such file or directory
Unable to init server: Could not connect: Connection refused
Error: cannot open display: :0
hawat@doge:~$